Question

A balance measures mass to \(0.001 \mathrm{~g}\). If you determine the mass of an object that weighs about \(30 \mathrm{~g}\), would you record the mass as \(30 \mathrm{~g}, 32.5 \mathrm{~g}, 31.25 \mathrm{~g}, 31.075 \mathrm{~g}\), or \(3000 \mathrm{~g}\) ? Explain your choice by writing two to three complete sentences that describe your thinking.

Short answer

The mass is \(31.075 \text{g}\) as it reflects the balance's precision and is approximately \(30 \text{g}\).

Step-by-step solution

- Understanding the Precision of the Balance

The balance measures mass to the nearest \(0.001 \text{g}\). This means it can give a reading with three decimal places of precision.

- Analyzing Each Option for Approximate Mass

The given options are \(30 \text{g}, 32.5 \text{g}, 31.25 \text{g}, 31.075 \text{g},\) and \(3000 \text{g}\). We need to determine which of these values correctly reflects the balance's precision and is approximately \(30 \text{g}\).

- Evaluating Each Option

- \(30 \text{g}\): This is not correct as it lacks the required precision.- \(32.5 \text{g}\): This has only one decimal place and is approximately \(30 \text{g}\) but lacks precision.- \(31.25 \text{g}\): This has two decimal places and is approximately \(30 \text{g}\) but lacks precision.- \(31.075 \text{g}\): This has three decimal places, indicating a reading to the nearest \(0.001 \text{g}\), and is approximately \(30 \text{g}\), making it the best match.- \(3000 \text{g}\): This is clearly too large and not approximately \(30 \text{g}\).

- Selecting the Most Accurate Answer

Given the analysis, the balance’s limit of precision is \(0.001 \text{g}\) and the option that best fits both precision and proximity to \(30 \text{g}\) is \(31.075 \text{g}\).

Key concepts

mass measurement

Mass measurement is a fundamental concept in science and engineering, which involves determining the quantity of matter in an object. The precise measurement of mass is crucial for experiments and calculations. When using a balance to measure mass, accuracy is important to ensure reliable data. Different balances have varying precision levels, from general kitchen scales to highly sensitive analytical balances.
In this exercise, the balance can measure mass to the nearest 0.001 grams. This implies high precision, which is essential for scientific accuracy. High precision balances help avoid experimental errors by providing exact mass values.

significant figures

Significant figures are the digits in a measurement that contribute to its precision. They include all known digits plus one estimated digit. The number of significant figures indicates the certainty of the measurement.
When recording mass, it is important to include the correct number of significant figures based on the precision of your measuring instrument. For example, if a balance measures up to three decimal places, such as 31.075 grams, then five significant figures must be recorded. This precision helps others understand the exactness of the measurement.
Each digit in a significant figure represents a reliable piece of information, ensuring that scientific data is both accurate and trustworthy.

balance precision

Balance precision is the smallest unit a balance can measure accurately. It determines how finely tuned the balance is and its capability to give reliable results. For instance, a balance with a precision of 0.001 grams can detect minute differences in mass that less precise instruments might miss.
In this task, the balance’s precision is crucial in deciding the correct mass measurement. Among the options presented, only 31.075 grams aligns with the balance's precision, showcasing the importance of understanding the instrument's capability when interpreting measurement results.

decimal places

Decimal places are the digits that appear after the decimal point in a number. They indicate the level of precision of a measurement. More decimal places mean higher precision. For example, a measurement of 31.075 grams is more precise than 31.25 grams because it has three decimal places compared to two.
In scientific measurements, recording the correct number of decimal places is vital for accuracy. In this scenario, a balance that measures to 0.001 grams requires mass values to be recorded up to three decimal places. This ensures that the measurement is as precise as the instrument allows, providing detailed and accurate data for scientific analysis.